Two-beam spectral interferometry (SI) has enabled the rapid development of such techniques as spectrometer-based frequency-domain optical coherence tomography (FD-OCT) and femtosecond pulse characterization. The Czerny-Turner spectrometer is a commonly used instrument in SI because, by definition, only two spherical mirrors and a plane grating can be configured in a coma-free geometry where, together with a low numerical aperture, spherical aberration can be avoided (see FIG. 1 illustrating known Czerny-Turner Spectrometer. However, such an optical design and layout does not provide resolution better than 0.1 nm, which is advantageous and typically necessary in the application of FD-OCT to obtain 1 mm imaging depth in skin, for example, with submicron axial resolution.
Czerny and Turner first showed that the coma aberration introduced by the off-axis reflection from a spherical mirror can be corrected by a symmetrical, but oppositely oriented, spherical mirror for spectrometer design. After that, Shafer showed that the coma aberration could be corrected in the Czerny-Turner spectrometer, even though its symmetry is broken, if the geometry parameters satisfy a condition that is known as the Shafer equation (see A. B. Shafer, L. R. Megill, and L. Droppleman, “Optimization of the Czerny-Turner spectrometer,” J. Opt. Soc. Am. 54 879-887 (1964); Q. Xue, S. Wang, and F. Lu, “Aberration-corrected Czerny-Turner imaging spectrometer with a wide spectral region,” Appl. Opt. 48, 11-16 (2009)). However, astigmatism remains in both configurations yielding different focal lengths in the tangential and sagittal planes. The astigmatism can be ignored in one-dimensional (1-D) spectroscopy by locating an exit slit at the tangential focal plane. However, some applications sensitive to power efficiency, such as high speed spectrometer-based FD-OCT, for example, required collecting the most power with high speed line CCD or CMOS cameras where the width of the detector area is limited to maximize signal to noise ratio. In those applications, the uncorrected astigmatism results in degraded performance. Reported methods to reduce or remove the limiting astigmatism include: using additional convex mirrors; placing compensating optics before the entrance slit; using toroidal mirrors; using a cylindrical grating; or introducing divergent illumination. Some techniques were pursued with a goal of providing extended spectral range. However, these methods need to satisfy a condition of the parameters of the Czerny-Turner spectrometer to compensate the astigmatism of the spectrometer, which may limit the spectrometer design for various specifications.
In view of the foregoing problems and shortcomings discussed above, the inventors have recognized the benefits and advantages of a solution thereto. The inventive solution proposes a modified Czerny-Turner geometry using only off-the-shelf, low-cost optical components without requiring the aforementioned restrictive condition.